How do they get this answer?

Question

What proportion of the students scoring between 292 and 310 in Professor Zangs?
ZANG: MEAN: 295 STANDARD DEVIATION: 13

Answer: .4659 or 47%

Answer 1

they used a z-score table to find the portion of the population between 3/13 s.d below the mean, and 15/13 s.d. above the mean

3/13 = .231 s.d. ... z-score below mean

15/13 = 1.154 s.d. ... z-score above mean

take the z-scores into the table, and it will give the portion of the population that lies in the range

add the two portions (above and below the mean)